Sieve of Eratosthenes

D Vautier
1/2023

The sieve of Eratosthenes is a popular way to develop prime numbers.  These are numbers evenly divisible by themselves and one, excluding one.  Two is the first prime.

So what is the big deal about prime numbers?  Actually there wasn’t any big deal about them, at least there wasn’t until the advent of cyber security and encryption when they finally found some usefulness.  Before that time it seems that school marms and math freaks alike enjoyed some perverse pleasure in over-empathizing the whole prime thing to suffering freshmen high students as if there were some kind of magic in those numbers.  There is not.  It’s mostly a curiosity.  We, of course, had to endure the whole madness of algebraic factoring; a mental exercise in doing something that goes nowhere and has no practical consequence except in some arcane fields of engineering.

So Eratosthenes set up a row of infinite numbers starting with two. He ignored the number one because it would have destroyed his number table. He looked at two and removed all numbers in the table divisible by two thus reducing his infinite table of consecutive numbers to an infinite table of odd numbers.  He looked at three and removed all following numbers divisible by three. He then looked at the next number which was five and continued the process.  The result eventually would be an infinite table of prime numbers.

Computers today do this very fast, however they never finish the job because there will always be an infinite number left to do.